' Generates Simple Latin Cubes, Horizontal Latin Diagonal Squares
' Tested with Office 365 under Windows 10
Sub LtnCbs4a()
Dim a(64), b(4)
y = MsgBox("Locked", vbCritical, "Routine LtnCbs4a")
End
n2 = 0: n9 = 0: k1 = 1: k2 = 1
m1 = 0: m2 = 3: s1 = 6
ShtNm1 = "LtnLns4"
' Generate data
Sheets("Klad1").Select
t1 = Timer
For j100 = 2 To 49 'Plane 1 (Top)
For i1 = 1 To 16
a(i1 + 48) = Sheets(ShtNm1).Cells(j100, i1).Value
Next i1
For j200 = 2 To 49 'Plane 2
If j200 = j100 Then GoTo 2000
For i1 = 1 To 16
a(i1 + 32) = Sheets(ShtNm1).Cells(j200, i1).Value
Next i1
' Check Identical Integers
For i1 = 1 To 16
If a(i1 + 48) = a(i1 + 32) Then GoTo 2000
Next i1
' Plane 3
For j32 = m1 To m2 'a(32)
a(32) = j32
If a(32) = a(48) Or a(32) = a(64) Then GoTo 320
a(27) = -2 * s1 + a(32) + a(40) + a(43) + a(44) - a(45) + 2 * a(48) + a(54) + a(59) + 2 * a(64):
If a(27) < 0 Or a(27) > 3 Then GoTo 320:
For j31 = m1 To m2 'a(31)
a(31) = j31
If a(31) = a(47) Or a(31) = a(63) Then GoTo 310
For j30 = m1 To m2 'a(30)
a(30) = j30
If a(30) = a(46) Or a(30) = a(62) Then GoTo 300
a(29) = s1 - a(30) - a(31) - a(32)
If a(29) < 0 Or a(29) > 3 Then GoTo 300 'a(29)
If a(29) = a(45) Or a(29) = a(61) Then GoTo 300
b(1) = a(32): b(2) = a(31): b(3) = a(30): b(4) = a(29): GoSub 860: If fl1 = 0 Then GoTo 300
a(26) = a(29) - a(40) + a(42) - a(44) + 2 * a(45) - a(48) + a(56) + a(60) - a(62) - a(63):
If a(26) < 0 Or a(26) > 3 Then GoTo 300:
For j28 = m1 To m2 'a(28)
a(28) = j28
If a(28) = a(44) Or a(28) = a(60) Then GoTo 280
a(25) = s1 - a(26) - a(27) - a(28): If a(25) < 0 Or a(25) > 3 Then GoTo 280:
a(24) = s1 - a(28) + a(29) - a(32) - a(40) - a(44) + a(45) - a(48):
If a(24) < 0 Or a(24) > 3 Then GoTo 280:
a(23) = s1 - a(29) - a(42) - a(45) + a(54) + a(59) - 2 * a(61):
If a(23) < 0 Or a(23) > 3 Then GoTo 280:
a(22) = s1 - a(23) - a(26) - a(27): If a(22) < 0 Or a(22) > 3 Then GoTo 280:
a(21) = s1 - a(22) - a(23) - a(24): If a(21) < 0 Or a(21) > 3 Then GoTo 280:
a(20) = s1 - a(24) - a(28) - a(32): If a(20) < 0 Or a(20) > 3 Then GoTo 280:
a(19) = s1 - a(23) - a(27) - a(31): If a(19) < 0 Or a(19) > 3 Then GoTo 280:
a(18) = s1 - a(22) - a(26) - a(30): If a(18) < 0 Or a(18) > 3 Then GoTo 280:
a(17) = s1 - a(18) - a(19) - a(20): If a(17) < 0 Or a(17) > 3 Then GoTo 280:
' Plane 4
a(16) = s1 - a(32) - a(48) - a(64): If a(16) < 0 Or a(16) > 3 Then GoTo 280:
a(15) = s1 - a(31) - a(47) - a(63): If a(15) < 0 Or a(15) > 3 Then GoTo 280:
a(14) = s1 - a(30) - a(46) - a(62): If a(14) < 0 Or a(14) > 3 Then GoTo 280:
a(13) = s1 - a(29) - a(45) - a(61): If a(13) < 0 Or a(13) > 3 Then GoTo 280:
a(12) = s1 - a(28) - a(44) - a(60): If a(12) < 0 Or a(12) > 3 Then GoTo 280:
a(11) = s1 - a(27) - a(43) - a(59): If a(11) < 0 Or a(11) > 3 Then GoTo 280:
a(10) = s1 - a(26) - a(42) - a(58): If a(10) < 0 Or a(10) > 3 Then GoTo 280:
a(9) = s1 - a(25) - a(41) - a(57): If a(9) < 0 Or a(9) > 3 Then GoTo 280:
a(8) = s1 - a(24) - a(40) - a(56): If a(8) < 0 Or a(8) > 3 Then GoTo 280:
a(7) = s1 - a(23) - a(39) - a(55): If a(7) < 0 Or a(7) > 3 Then GoTo 280:
a(6) = s1 - a(22) - a(38) - a(54): If a(6) < 0 Or a(6) > 3 Then GoTo 280:
a(5) = s1 - a(21) - a(37) - a(53): If a(5) < 0 Or a(5) > 3 Then GoTo 280:
a(4) = s1 - a(20) - a(36) - a(52): If a(4) < 0 Or a(4) > 3 Then GoTo 280:
a(3) = s1 - a(19) - a(35) - a(51): If a(3) < 0 Or a(3) > 3 Then GoTo 280:
a(2) = s1 - a(18) - a(34) - a(50): If a(2) < 0 Or a(2) > 3 Then GoTo 280:
a(1) = s1 - a(17) - a(33) - a(49): If a(1) < 0 Or a(1) > 3 Then GoTo 280:
' Exclude solutions with identical numbers in rows, colums or pillars
GoSub 800: If fl1 = 0 Then GoTo 280 'rows, colums or pillars
'Space Diagonals, Diagonals Hor Magic Planes
n9 = n9 + 1: GoSub 740 'Print results (selected numbers)
'' n9 = n9 + 1: GoSub 750 'Print results (planes 1, 2, 3, 4)
280 Next j28
300 Next j30
310 Next j31
320 Next j32
2000 Next j200
1000 Next j100
t2 = Timer
t10 = Str(t2 - t1) + " sec., " + Str(n9) + " Solutions for sum" + Str(s1)
y = MsgBox(t10, 0, "Routine LtnCbs4a")
End
' Print results (selected numbers)
740 For i1 = 1 To 64
Cells(n9, i1).Value = a(i1)
Next i1
Cells(n9, 65).Value = j100
Cells(n9, 66).Value = j200
Cells(n9, 67).Value = n9
Return
' Print results (planes 11, 12, 13 and 14)
750 n2 = n2 + 1
If n2 = 9 Then
n2 = 1: k1 = k1 + 20: k2 = 1
Else
If n9 > 1 Then k2 = k2 + 5
End If
Cells(1, 1).Value = n9
Cells(k1, k2 + 1).Font.Color = -4165632
Cells(k1, k2 + 1).Value = CStr(n9)
Cells(k1, k2 + 2).Value = j100
Cells(k1, k2 + 3).Value = j200
For i0 = 1 To 4
i3 = (4 - i0) * 16
For i1 = 1 To 4
For i2 = 1 To 4
i3 = i3 + 1
Cells(k1 + i1 + (i0 - 1) * 5, k2 + i2).Value = a(i3)
Next i2
Next i1
Next i0
Return
' Exclude solutions with identical numbers in rows, colums or pillars
' Space Diagonals, Diagonals Hor. Magic Planes
800 fl1 = 1
' Rows
i1 = -3
For i0 = 1 To 16
i1 = i1 + 4
b(1) = a(i1): b(2) = a(i1 + 1): b(3) = a(i1 + 2): b(4) = a(i1 + 3)
GoSub 860
If fl1 = 0 Then Return
Next i0
' Columns
i1 = 0: i2 = 0
For i0 = 1 To 16
i1 = i1 + 1
b(1) = a(i1): b(2) = a(i1 + 4): b(3) = a(i1 + 8): b(4) = a(i1 + 12)
i2 = i2 + 1: If i2 = 4 Then i2 = 0: i1 = i1 + 12
GoSub 860
If fl1 = 0 Then Return
Next i0
' Pillars
i1 = 0: i2 = 0
For i0 = 1 To 16
i1 = i0
b(1) = a(i1): b(2) = a(i1 + 16): b(3) = a(i1 + 32): b(4) = a(i1 + 48)
GoSub 860
If fl1 = 0 Then Return
Next i0
' Space Diagonals
b(1) = a(1): b(2) = a(22): b(3) = a(43): b(4) = a(64): GoSub 860: If fl1 = 0 Then Return
b(1) = a(4): b(2) = a(23): b(3) = a(42): b(4) = a(61): GoSub 860: If fl1 = 0 Then Return
b(1) = a(13): b(2) = a(26): b(3) = a(39): b(4) = a(52): GoSub 860: If fl1 = 0 Then Return
b(1) = a(16): b(2) = a(27): b(3) = a(38): b(4) = a(49): GoSub 860: If fl1 = 0 Then Return
' Diagonals Hor Magic Planes
b(1) = a(1): b(2) = a(6): b(3) = a(11): b(4) = a(16): GoSub 860: If fl1 = 0 Then Return
b(1) = a(4): b(2) = a(7): b(3) = a(10): b(4) = a(13): GoSub 860: If fl1 = 0 Then Return
b(1) = a(17): b(2) = a(22): b(3) = a(27): b(4) = a(32): GoSub 860: If fl1 = 0 Then Return
b(1) = a(20): b(2) = a(23): b(3) = a(26): b(4) = a(29): GoSub 860: If fl1 = 0 Then Return
b(1) = a(33): b(2) = a(38): b(3) = a(43): b(4) = a(48): GoSub 860: If fl1 = 0 Then Return
b(1) = a(36): b(2) = a(39): b(3) = a(42): b(4) = a(45): GoSub 860: If fl1 = 0 Then Return
b(1) = a(49): b(2) = a(54): b(3) = a(59): b(4) = a(64): GoSub 860: If fl1 = 0 Then Return
b(1) = a(52): b(2) = a(55): b(3) = a(58): b(4) = a(61): GoSub 860: If fl1 = 0 Then Return
Return
' Diagonals Vert Magic Planes L/R (Option)
'' b(1) = a(1): b(2) = a(21): b(3) = a(41): b(4) = a(61): GoSub 860: If fl1 = 0 Then Return
'' b(1) = a(13): b(2) = a(25): b(3) = a(37): b(4) = a(49): GoSub 860: If fl1 = 0 Then Return
'' b(1) = a(2): b(2) = a(22): b(3) = a(42): b(4) = a(62): GoSub 860: If fl1 = 0 Then Return
'' b(1) = a(14): b(2) = a(26): b(3) = a(38): b(4) = a(50): GoSub 860: If fl1 = 0 Then Return
'' b(1) = a(3): b(2) = a(23): b(3) = a(43): b(4) = a(63): GoSub 860: If fl1 = 0 Then Return
'' b(1) = a(15): b(2) = a(27): b(3) = a(39): b(4) = a(51): GoSub 860: If fl1 = 0 Then Return
'' b(1) = a(4): b(2) = a(24): b(3) = a(44): b(4) = a(64): GoSub 860: If fl1 = 0 Then Return
'' b(1) = a(16): b(2) = a(28): b(3) = a(40): b(4) = a(52): GoSub 860: If fl1 = 0 Then Return
' Diagonals Vert Magic Planes B/F (Option)
'' b(1) = a(1): b(2) = a(18): b(3) = a(35): b(4) = a(52): GoSub 860: If fl1 = 0 Then Return
'' b(1) = a(4): b(2) = a(19): b(3) = a(34): b(4) = a(49): GoSub 860: If fl1 = 0 Then Return
'' b(1) = a(5): b(2) = a(22): b(3) = a(39): b(4) = a(56): GoSub 860: If fl1 = 0 Then Return
'' b(1) = a(8): b(2) = a(23): b(3) = a(38): b(4) = a(53): GoSub 860: If fl1 = 0 Then Return
'' b(1) = a(9): b(2) = a(26): b(3) = a(43): b(4) = a(60): GoSub 860: If fl1 = 0 Then Return
'' b(1) = a(12): b(2) = a(27): b(3) = a(42): b(4) = a(57): GoSub 860: If fl1 = 0 Then Return
'' b(1) = a(13): b(2) = a(30): b(3) = a(47): b(4) = a(64): GoSub 860: If fl1 = 0 Then Return
'' b(1) = a(16): b(2) = a(31): b(3) = a(46): b(4) = a(61): GoSub 860: If fl1 = 0 Then Return
Return
860 fl1 = 1
For j1 = 1 To 4
b2 = b(j1)
For j2 = (1 + j1) To 4
If b2 = b(j2) Then fl1 = 0: Return
Next j2
Next j1
Return
End Sub
